I know that merely memorizing book moves is not good; one should understand the concepts behind each move he or she makes. However, I was in a very large, very important tournament recently. I didn't want to risk playing inferior moves, so I repeated book moves. Luckily, I had been studying the opening (Two Knights) the night before. I got to a position where Nick deFirmian says in Modern Chess Openings edition 14 the position is -/+, so Black should be way better. However, even with such a "good" position, I narrowly lost the game. In a -/+ game I should be able to win easily. Why am I better (I have the black pieces)?

Don't be too hard on yourself, the evaluation was too generous for Black. I took your question to the source, Nick deFirmian, who will be coming out with the 15th Edition shortly. This is what Nick had to say:

Regarding Chris's question, it looks to me that the position is unclear instead of -/+, which must be some old evaluation. After 15 dxe4 Nc5 16 Nc3 Ba6 the 15th Edition will evaluate this as about even. I find that the computer likes White a lot until you analyze for some moves and it "realizes" that there are problems with the White king stuck in the center.

Note that in any reference work there will be some lines and evaluations passed down through time that may need correction. When following a line, you should come out confident that you understand and agree with the assessment. In this case, White's development is backward and his king is stuck in the center, but with three pawns invested Black does not have an easy task. My gut tells me Black should come out on top but any misstep will cost either side dearly (pity you didn't provide the whole game).

I like that you appreciate memorizing opening moves is insufficient to prepare yourself for tournament play. It is especially important to understand the nature of the opening that you play. The Two Knights Defense is an aggressive, counterattacking opening. You have to be comfortable sacrificing a pawn for an initiative. This particular line is an especially greedy treatment for White. The move 12.Nf3 is particularly rare, with only about five examples in the database.

Black can also play for a slower buildup with 13... Rb6, maintaining the kingside majority for future use.

Position after 13...Rb6

It is perhaps noteworthy that 13... Rb6 was played in the most recent game I have (both players were about 2350):